Assessing methods to disaggregate daily precipitation for hydrological simulation Peng Gao, Gregory Carbone, Daniel Tufford, Aashka Patel, and Lauren Rouen Department of Geography University of South Carolina
Background CISA (Carolinas Integrated Sciences and Assessments) incorporates climate information into water and coastal management Hydrological modeling: how climate affects water supply and quality
Background Continuous simulation modeling (e.g. Hydrologic Simulation Program-Fortran (HSPF)) an important tool to investigate the impacts of climate change on water resources high spatial and temporal resolution (e.g. hourly or subdaily) rainfall data
Challenges - the constraint of data availability Precipitation data are often available only at coarser levels (i.e., daily) (25,000 daily recording stations, 8,000 hourly stations in U.S.) (Booner, 1998)
Challenges - the constraint of data availability Meteorological variables from the GCMs (General Circulation Models ) needed for hydrological simulation - typically at monthly or daily scales
Rainfall Depth (in) Solutions Disaggregate the daily rainfall to hourly time series Date Jun 16 0 Prec. (inch) 0.035 Jun 17 0.1 Jun 18 0 0.03 0.025 0.02 0.015 0.01 et al. 0.005 0 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 Hours
Background Many disaggregation methods Few tests to assess the performance of these methods on hydrological simulations
Overview of the Study Examine three different disaggregation methods to construct hourly precipitation time series from daily precipitation Use those time series as input and compare simulated flows against observed flows
Three Disaggregation Methods
Method1 Triangular by HSPF Daily rainfall needs to be disaggregated: 0.10 daily total 0 0.01 0.02 0.04 0.08 0.16 0.32 10 0 0 0 0 0 0.01 0.01 11 0 0 0 0.01 0.01 0.04 0.05 0.00625 0.025 0.0375 0.025 0.00625 0 ratio for each hour 12 0 0.01 0.01 0.02 0.03 0.06 0.1 13 0 0 0.01 0.01 0.03 0.04 0.1 14 0 0 0 0 0.01 0.01 0.05 15 0 0 0 0 0 0 0.01 Find the daily total closest to but larger than the daily rainfall that needs to be disaggregated Distribute the daily rainfall proportionally to ratio for each hour
Method 2 and 3 It iteratively searches the rainfall events from the existing rainfall event database until the remaining amount is lower than an assigned minimum threshold Advantage:reserving the probability distribution
Rainfall Depth (in) To disaggregate a 0.083 inch daily total with the assigned minimum threshold: 0.015 inch Rainfall Depth (in) 0.035 0.03 0.025 0.02 0.015 0.01 0.005 0 Remaining = 0.073-0.04 = 0.033 Remaining = 0.083-0.001 = 0.073 Remaining = 0.033-0.02 = 0.013 < 0.015 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 Hours Rainfall events Total: 0.04 inch (0.01 inch at 3 o clock and 0.03 inch at 4 0 clock) Total: 0.02 inch (0.02 inch at 8 o clock) Total: 0.01 inch (0.01 inch at 9 o clock) Total: 0.01 inch (0.01 Event3 inch at 6 o clock) Total: Event2 0.01 inch (0.01 inch at 17 o Event1 clock) et al. How to deal with the remaining amount of 0.013 inch?
Rainfall Depth (in) Method2: Socolofsky method The remaining amount follows exponential distribution (e.g. Modeled remaining amount = - Actual remaining amount (i.e., -0.013)*log (random seed) at random hour from (0 to23) ) 0.035 0.03 Modeled Daily total: 0.088 inch 0.083 inch 0.025 0.02 0.015 0.01 0.005 Remaining amount 0.018 Event3 Event2 Event1 0 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 Hours Actual Daily total: 0.083 inch
Rainfall Depth (in) Method3: Adjusted Socolofsky method The remaining amount is directly placed into a onehour storm event 0.035 0.03 Modeled Daily total: 0.083 inch 0.025 0.02 0.015 0.01 0.005 Remaining amount 0.013 Event3 Event2 Event1 0 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 Hours Actual Daily total: 0.083 inch
Rainfall Depth (in) Rainfall Depth (in) Rainfall Depth (in) 0.035 0.03 0.025 0.02 0.015 0.01 0.005 0 0.035 0.03 0.025 0.02 0.015 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 Hours Event3 Event2 Event1 Remaining Amount Event3 Daily total: 0.083 inch Triangular Distribution Socolofsky method 0.01 Event2 0.005 Event1 0 0.035 0.03 0.025 0.02 0.015 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 Hours Remaining Amount Event3 Adjusted Socolofsky method 0.01 Event2 0.005 Event1 0 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 Hours
Characteristics Comparison Triangular Distribution Socolofsky Method Adjusted Socolofsky Method Stochastic N Y Y Using existing hourly data Conserve daily total Conserve PDF N Y Y Y N Y N Y Y Multi events N Possible Possible
Observed Hourly Precipitation Design Sum to Daily Precipitation HSPF Simulated Stream Flow Disaggregate Disaggregated Precipitation Observed Stream Flow
Observed Hourly Precipitation Virtual station: area weighted mean of stations whose Thiessen polygons fall into the watershed
Rainfall Depth (in) Rainfall Depth (in) 0.035 Disaggregated Precipitation Triangular Distribution Ten simulations for each Socolofsky method and Adjusted Socolofsky method using precipitation from the virtual station as the existing rainfall event database Simulation 1 0.03 0.025 0.02 0.015 0.035 0.03 Rest Amount Event3 Simulation 2 0.01 0.005 0 0.025 0.02 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 0.015 23 Event2 Event1 Rest Amount Hours 0.01 Event3 Event2 0.005 0 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 Event1 Hours
Comparisons Four types of hourly precipitation time series Precipitation from the virtual station ( a combination of observed hourly precipitation) Triangular distribution Socolofsky Method (ten simulations) Adjusted Socolofsky Method (ten simulations) The simulated stream flows VS. the observed stream flows in the verification time period
Study Area
Model performance evaluation How close the simulated flows to observed flows index of agreement (d) (higher, better) mean absolute error (MAE) (lower, better) Nash-Sutcliff efficiency (NS) (closer to 1, better) percent bias (p-bias) (lower, better) root mean squared error (RMSE) (lower, better) Weather simulated flows follow the same distribution Mann-Whitney-Wilcoxon Test
Results Socolofsky (S) and Adjusted Socolofsky (AS) VS. Virtual station (V)
Statistic of daily stream flow in watershed South Yadkin, NC Results d MAE NS p-bias RMSE V 0.89 83.10 0.64-15.47 186.8 S1 0.86 87.60 0.57-15.48 204.7 S2 0.79 93.66 0.40-18.10 241.3 S3 0.86 86.43 0.58-10.27 202.2 S4 0.84 83.09 0.51-8.91 218.3 S5 0.81 82.70 0.48-11.40 225.4 S6 0.78 105.15 0.30-26.64 260.2 S7 0.76 92.13 0.32-10.23 256.5 S8 0.78 100.31 0.35-25.47 251.9 S9 0.81 93.72 0.42-15.36 236.6 S10 0.86 87.46 0.58-17.88 201.8 d MAE NS p-bias RMSE V 0.89 83.10 0.64-15.47 186.8 AS1 0.84 87.68 0.51-14.22 217.8 AS2 0.84 86.53 0.54-13.47 210.2 AS3 0.82 87.20 0.48-13.74 224.1 AS4 0.82 91.19 0.47-14.45 227.3 AS5 0.86 83.31 0.59-12.86 199.3 AS6 0.85 84.10 0.56-12.73 206.5 AS7 0.86 84.76 0.59-13.32 200.0 AS8 0.82 88.52 0.47-13.76 227.0 AS9 0.83 90.31 0.49-14.35 222.5 AS10 0.83 85.77 0.51-13.18 217.4 Socolofsky (S) and Adjusted Socolofsky (AS) produced similar statistics to precipitation from the virtual station (V)
Statistic of daily stream flow in watershed South Yadkin, NC Results d MAE NS p-bias RMSE V 0.89 83.10 0.64-15.47 186.8 S1 0.86 87.60 0.57-15.48 204.7 S2 0.79 93.66 0.40-18.10 241.3 S3 0.86 86.43 0.58-10.27 202.2 S4 0.84 83.09 0.51-8.91 218.3 S5 0.81 82.70 0.48-11.40 225.4 S6 0.78 105.15 0.30-26.64 260.2 S7 0.76 92.13 0.32-10.23 256.5 S8 0.78 100.31 0.35-25.47 251.9 S9 0.81 93.72 0.42-15.36 236.6 S10 0.86 87.46 0.58-17.88 201.8 d MAE NS p-bias RMSE V 0.89 83.10 0.64-15.47 186.8 AS1 0.84 87.68 0.51-14.22 217.8 AS2 0.84 86.53 0.54-13.47 210.2 AS3 0.82 87.20 0.48-13.74 224.1 AS4 0.82 91.19 0.47-14.45 227.3 AS5 0.86 83.31 0.59-12.86 199.3 AS6 0.85 84.10 0.56-12.73 206.5 AS7 0.86 84.76 0.59-13.32 200.0 AS8 0.82 88.52 0.47-13.76 227.0 AS9 0.83 90.31 0.49-14.35 222.5 AS10 0.83 85.77 0.51-13.18 217.4 Socolofsky (S) varied more than Adjusted Socolofsky (AS) because it does not conserve the depth of daily rainfall
Triangular (T) VS. Virtual station (V) Results South Yadkin Upper Broad South Fork Tyger Black d MAE NS p-bias RMSE V 0.89 83.10 0.64-15.47 186.82 T 0.86 92.99 0.51-15.66 219.06 V 0.89 132.50 0.57-27.68 216.87 T 0.88 133.17 0.44-28.51 246.93 V 0.91 210.76 0.70 7.46 441.91 T 0.92 220.83 0.73 8.07 420.78 V 0.86 324.46 0.60 12.02 702.24 T 0.91 313.87 0.68 11.32 634.96 V 0.89 387.23 0.69-18.73 656.19 T 0.91 332.88 0.75-9.14 586.33 The performance of Triangular (T) is not consistent
Results Distribution of Simulated Flows Mann-Whitney-Wilcoxon Test Socolofsky (S) and Adjusted Socolofsky (AS) VS. Virtual station (V) no difference Triangular (T) VS. Virtual station (V) significant difference
Conclusion The adjusted Socolofsky method most robust in terms of performance when compared to the model verification run a useful means of disaggregating the daily precipitation from GCMs under different scenarios
Acknowledges Department of Geography, CISA, Geography Graduate Student Association provides travel fundings